Theorems · Theorem · general topology
interior_iInter_subset
∀ {X : Type u} [inst : TopologicalSpace X] {ι : Sort v} (s : ι → Set X), interior (⋂ i, s i) ⊆ ⋂ i, interior (s i)- Defined in
- Mathlib.Topology.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.iInterstatement · cited by 1,084
- interiorstatement · cited by 714
- Set.iInter_subsetproof · cited by 39
- interior_monoproof · cited by 38
- Set.subset_iInterproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- interior_iInter₂_subsetproof · cited by 1